docs: def friction_plate_Kumar(Re, chevron_angle):
      r'''Calculates Darcy friction factor for single-phase flow in a 
      **well-designed** Chevron-style plate heat exchanger according to [1]_.
      The data is believed to have been developed by APV International Limited,
      since acquired by SPX Corporation. This uses a curve fit of that data
      published in [2]_.
      
      .. math::
          f_f = \frac{C_2}{Re^p}
          
      C2 and p are coefficients looked up in a table, with varying ranges
      of Re validity and chevron angle validity. See the source for their
      exact values.
          
      Parameters
      ----------
      Re : float
          Reynolds number with respect to the hydraulic diameter of the channels,
          [-]
      chevron_angle : float
          Angle of the plate corrugations with respect to the vertical axis
          (the direction of flow if the plates were straight), between 0 and
          90. Many plate exchangers use two alternating patterns; use their
          average angle for that situation [degrees]
          
      Returns
      -------
      fd : float
          Darcy friction factor [-]
  
      Notes
      -----
      Data on graph from Re=0.1 to Re=10000, with chevron angles 30 to 65 degrees.
      See `PlateExchanger` for further clarification on the definitions.
      
      It is believed the constants used in this correlation were curve-fit to
      the actual graph in [1]_ by the author of [2]_ as there is no 
      
      The length the friction factor gets multiplied by is not the flow path
      length, but rather the straight path length from port to port as if there
      were no chevrons.
      
      As the coefficients change, there are numerous small discontinuities, 
      although the data on the graphs is continuous with sharp transitions
      of the slope.
      
      The author of [1]_ states clearly this correlation is "applicable only to 
      well designed Chevron PHEs".
      
      Examples
      --------
      >>> friction_plate_Kumar(Re=2000, chevron_angle=30)
      2.9760669055634517
  
      References
      ----------
      .. [1] Kumar, H. "The plate heat exchanger: construction and design." In 
         First U.K. National Conference on Heat Transfer: Held at the University 
         of Leeds, 3-5 July 1984, Institute of Chemical Engineering Symposium 
         Series, vol. 86, pp. 1275-1288. 1984.
      .. [2] Ayub, Zahid H. "Plate Heat Exchanger Literature Survey and New Heat
         Transfer and Pressure Drop Correlations for Refrigerant Evaporators." 
         Heat Transfer Engineering 24, no. 5 (September 1, 2003): 3-16. 
         doi:10.1080/01457630304056.
      '''
      beta_list_len = len(Kumar_beta_list)
      
      for i in range(beta_list_len):
          if chevron_angle <= Kumar_beta_list[i]:
              C2_options, p_options, Re_ranges = Kumar_C2s[i], Kumar_Ps[i], Kumar_fd_Res[i]
              break
          elif i == beta_list_len-1:
              C2_options, p_options, Re_ranges = Kumar_C2s[-1], Kumar_Ps[-1], Kumar_fd_Res[-1]
                  
      Re_len = len(Re_ranges)
      
      for j in range(Re_len):
          if Re <= Re_ranges[j]:
              C2, p = C2_options[j], p_options[j]
              break
          elif j == Re_len-1:
              C2, p = C2_options[-1], p_options[-1]
          
      # Originally in Fanning friction factor basis
      return 4.0*C2*Re**-p